Neophobia analysis

Setup

Load and install R packages:

packages <- c('lmerTest', 'lme4', 'ggplot2', 'tidyverse', 'readxl', 'purrr', 'performance', 'emmeans', 'MASS', 'dplyr', 'tidyr')

# Check if each package is installed; if not, install it
for (pkg in packages) {
  if (!requireNamespace(pkg, quietly = TRUE)) {
    install.packages(pkg)
  }
  library(pkg, character.only = TRUE)
}

## Loading required package: lme4

## Loading required package: Matrix

## 
## Attaching package: 'lmerTest'

## The following object is masked from 'package:lme4':
## 
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## The following object is masked from 'package:stats':
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Data Loading

Grab neophobia_data.csv from processed_data directory:

script_dir <- dirname(rstudioapi::getActiveDocumentContext()$path)
# Set the working directory to the script's directory
setwd(script_dir)

data <- read.csv("processed_data/neophobia_data.csv", row.names = 1)

Quick Data Inspection

Summary statistics of the data:

# Quick look at structure
str(data)

## 'data.frame':    536 obs. of  15 variables:
##  $ Bird_ID         : chr  "BB_BB" "BB_BB" "BB_BB" "BB_BB" ...
##  $ Trial           : int  1 2 3 4 5 6 7 8 1 2 ...
##  $ Enclosure       : chr  "B8" "B8" "B8" "B8" ...
##  $ Object          : chr  "novel" "novel" "control" "control" ...
##  $ Context         : chr  "group" "individual" "group" "individual" ...
##  $ Latency_to_enter: num  2.2 6.23 2.27 1.57 1.07 ...
##  $ Latency_to_Eat  : num  2.9 13.83 2.2 3.73 2.73 ...
##  $ Zoi_duration    : num  183.7 91.9 85.4 203.3 371.5 ...
##  $ Object_Type     : int  2 4 3 3 1 5 3 3 5 1 ...
##  $ GroupID         : chr  "7A" NA "7A" NA ...
##  $ NestID          : chr  "2024VM08" "2024VM08" "2024VM08" "2024VM08" ...
##  $ group_dummy     : int  1 0 1 0 1 0 1 0 1 0 ...
##  $ ind_dummy       : int  0 1 0 1 0 1 0 1 0 1 ...
##  $ Object_contrast : num  0.5 0.5 -0.5 -0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 ...
##  $ Context_contrast: num  0.5 -0.5 0.5 -0.5 0.5 -0.5 0.5 -0.5 0.5 -0.5 ...

summary(data)

##    Bird_ID              Trial       Enclosure            Object         
##  Length:536         Min.   :1.00   Length:536         Length:536        
##  Class :character   1st Qu.:2.75   Class :character   Class :character  
##  Mode  :character   Median :4.50   Mode  :character   Mode  :character  
##                     Mean   :4.50                                        
##                     3rd Qu.:6.25                                        
##                     Max.   :8.00                                        
##    Context          Latency_to_enter  Latency_to_Eat     Zoi_duration   
##  Length:536         Min.   :  0.800   Min.   :  1.792   Min.   :  0.00  
##  Class :character   1st Qu.:  1.467   1st Qu.:  2.800   1st Qu.: 38.93  
##  Mode  :character   Median :  1.880   Median :  3.633   Median : 76.35  
##                     Mean   :  8.380   Mean   : 42.457   Mean   :128.20  
##                     3rd Qu.:  2.600   3rd Qu.:  5.684   3rd Qu.:162.03  
##                     Max.   :600.000   Max.   :600.000   Max.   :598.13  
##   Object_Type      GroupID             NestID           group_dummy 
##  Min.   :1.000   Length:536         Length:536         Min.   :0.0  
##  1st Qu.:2.000   Class :character   Class :character   1st Qu.:0.0  
##  Median :3.000   Mode  :character   Mode  :character   Median :0.5  
##  Mean   :2.787                                         Mean   :0.5  
##  3rd Qu.:4.000                                         3rd Qu.:1.0  
##  Max.   :5.000                                         Max.   :1.0  
##    ind_dummy   Object_contrast Context_contrast
##  Min.   :0.0   Min.   :-0.5    Min.   :-0.5    
##  1st Qu.:0.0   1st Qu.:-0.5    1st Qu.:-0.5    
##  Median :0.5   Median : 0.0    Median : 0.0    
##  Mean   :0.5   Mean   : 0.0    Mean   : 0.0    
##  3rd Qu.:1.0   3rd Qu.: 0.5    3rd Qu.: 0.5    
##  Max.   :1.0   Max.   : 0.5    Max.   : 0.5

Data Preprocessing

Missing Group ID Values

The GroupID values are currently coded as NA during individual trials. Assign the most frequent group for each bird:

most_frequent_group <- function(group_ids) {
  group_ids <- group_ids[!is.na(group_ids)]
  if (length(group_ids) == 0) return(NA)
  names(sort(table(group_ids), decreasing = TRUE))[1]
}

most_frequent_group_per_bird <- data %>%
  group_by(Bird_ID) %>%
  summarize(most_frequent_group = most_frequent_group(GroupID)) %>%
  ungroup()

data <- data %>%
  left_join(most_frequent_group_per_bird, by = "Bird_ID") %>%
  mutate(GroupID = ifelse(is.na(GroupID), most_frequent_group, GroupID)) %>%
  dplyr::select(-most_frequent_group)

Adjusting Trial Numbers, so the baseline is the first trial rather than 0.

Adjust the Trial variable by subtracting 1:

data$Trial <- data$Trial - 1

Statistical Modeling

1) Latency to Enter

The full model as described in the RR, includes Object_contrast, Context_contrast, and Trial, and a complex random effect structure:

enter_model <- lmer(Latency_to_enter ~ Object_contrast * Context_contrast + Trial + 
                (1 | NestID) + 
                (-1 + group_dummy | GroupID) + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data)

## boundary (singular) fit: see help('isSingular')

summary(enter_model)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_enter ~ Object_contrast * Context_contrast + Trial +  
##     (1 | NestID) + (-1 + group_dummy | GroupID) + (-1 + ind_dummy +  
##     group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 5712.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4529 -0.1408 -0.0422  0.0686 10.2384 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  Bird_ID  ind_dummy   1.198e+03 34.6124      
##           group_dummy 2.852e-02  0.1689  1.00
##  NestID   (Intercept) 0.000e+00  0.0000      
##  GroupID  group_dummy 0.000e+00  0.0000      
##  Residual             2.268e+03 47.6258      
## Number of obs: 536, groups:  Bird_ID, 67; NestID, 43; GroupID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                       17.4867     4.3340 279.0124   4.035 7.06e-05
## Object_contrast                    5.1073     4.1143 464.9955   1.241  0.21510
## Context_contrast                 -12.0511     5.8852  79.6165  -2.048  0.04389
## Trial                             -2.6020     0.9052 471.1684  -2.874  0.00423
## Object_contrast:Context_contrast  -9.7670     8.2292 464.9964  -1.187  0.23588
##                                     
## (Intercept)                      ***
## Object_contrast                     
## Context_contrast                 *  
## Trial                            ** 
## Object_contrast:Context_contrast    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.005                     
## Cntxt_cntrs -0.356  0.000              
## Trial       -0.731 -0.007  0.007       
## Objct_cn:C_ -0.010  0.000  0.000  0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

check_model(enter_model)

The random effect structure seems to be too complex for the amount of data. However, the variance for the (Intercept) under NestID is 0 and the variance for group_dummy under GroupID is 0. This suggests that both nest as differences between groups contribute minimally to the variance in the outcome model. Let’s drop both effects.

enter_model2 <- lmer(Latency_to_enter ~ Object_contrast * Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data)

## boundary (singular) fit: see help('isSingular')

summary(enter_model2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_enter ~ Object_contrast * Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 5712.3
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.4529 -0.1408 -0.0422  0.0686 10.2384 
## 
## Random effects:
##  Groups   Name        Variance  Std.Dev. Corr
##  Bird_ID  ind_dummy   1198.0356 34.6127      
##           group_dummy    0.0286  0.1691  1.00
##  Residual             2268.2114 47.6257      
## Number of obs: 536, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                  Estimate Std. Error       df t value Pr(>|t|)
## (Intercept)                       17.4867     4.3340 279.0054   4.035 7.06e-05
## Object_contrast                    5.1073     4.1143 464.9960   1.241  0.21510
## Context_contrast                 -12.0511     5.8852  79.6162  -2.048  0.04389
## Trial                             -2.6020     0.9052 471.1689  -2.874  0.00423
## Object_contrast:Context_contrast  -9.7670     8.2292 464.9969  -1.187  0.23588
##                                     
## (Intercept)                      ***
## Object_contrast                     
## Context_contrast                 *  
## Trial                            ** 
## Object_contrast:Context_contrast    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.005                     
## Cntxt_cntrs -0.356  0.000              
## Trial       -0.731 -0.007  0.007       
## Objct_cn:C_ -0.010  0.000  0.000  0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

check_model(enter_model2)

Seems like the interaction between object and context is non-significant, let’s drop it. Given the non-normal distribution, let’s logtransform the data as well:

enter_model3 <- lmer(log(Latency_to_enter) ~ Object_contrast + Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data)

## boundary (singular) fit: see help('isSingular')

summary(enter_model3)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log(Latency_to_enter) ~ Object_contrast + Context_contrast +  
##     Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 1123.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9335 -0.4596 -0.0811  0.3538  6.9301 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.307211 0.55427      
##           group_dummy 0.008857 0.09411  1.00
##  Residual             0.386408 0.62162      
## Number of obs: 536, groups:  Bird_ID, 67
## 
## Fixed effects:
##                   Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)        1.29304    0.06319 188.76075  20.464   <2e-16 ***
## Object_contrast    0.10177    0.05370 465.99922   1.895   0.0587 .  
## Context_contrast  -0.19502    0.07774  76.68931  -2.508   0.0142 *  
## Trial             -0.13771    0.01179 468.78462 -11.679   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_
## Objct_cntrs  0.004              
## Cntxt_cntrs -0.458  0.000       
## Trial       -0.653 -0.007  0.007
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

check_model(enter_model3)

There are still issues with the data distribution, let’s remove birds that did not interact and boxcox_transform:

data_enter <- data %>% filter(Latency_to_enter != 600)

boxcox_transform <- boxcox(lm(Latency_to_enter ~ Object_contrast + Context_contrast + Trial, data = data_enter))

best_lambda <- boxcox_transform$x[which.max(boxcox_transform$y)]

data_enter$Latency_to_enter_trans <- (data_enter$Latency_to_enter^best_lambda - 1) / best_lambda

enter_model4_boxcox <- lmer(Latency_to_enter_trans ~ Object_contrast + 
                              Context_contrast + Trial + 
                            (-1 + ind_dummy + group_dummy | Bird_ID), 
                            data = data_enter)
summary(enter_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_enter_trans ~ Object_contrast + Context_contrast +  
##     Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data_enter
## 
## REML criterion at convergence: -115.2
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -3.00860 -0.62234  0.05268  0.62220  2.42212 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.023257 0.15250      
##           group_dummy 0.007021 0.08379  0.84
##  Residual             0.037006 0.19237      
## Number of obs: 533, groups:  Bird_ID, 67
## 
## Fixed effects:
##                    Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)        0.686462   0.020720 165.959664  33.130   <2e-16 ***
## Object_contrast    0.007148   0.016674 395.856100   0.429    0.668    
## Context_contrast  -0.028455   0.020248  64.608541  -1.405    0.165    
## Trial             -0.051896   0.003669 424.210940 -14.146   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_
## Objct_cntrs  0.007              
## Cntxt_cntrs -0.301 -0.002       
## Trial       -0.623 -0.009  0.016

check_model(enter_model4_boxcox)

Comparing the different models, the boxcox transfromed comes out as best:

enter_model <- lmer(Latency_to_enter ~ Object_contrast * Context_contrast + Trial + 
                (1 | NestID) + 
                (-1 + group_dummy | GroupID) + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data_enter)

## boundary (singular) fit: see help('isSingular')

enter_model2 <- lmer(Latency_to_enter ~ Object_contrast * Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data_enter)

## boundary (singular) fit: see help('isSingular')

enter_model3 <- lmer(log(Latency_to_enter) ~ Object_contrast + Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data_enter)

## boundary (singular) fit: see help('isSingular')

enter_model4_boxcox <- lmer(Latency_to_enter_trans ~ Object_contrast + 
                              Context_contrast + Trial + 
                            (-1 + ind_dummy + group_dummy | Bird_ID), 
                            data = data_enter)


anova(enter_model, enter_model2, enter_model3, enter_model4_boxcox)

## refitting model(s) with ML (instead of REML)

## Data: data_enter
## Models:
## enter_model3: log(Latency_to_enter) ~ Object_contrast + Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## enter_model4_boxcox: Latency_to_enter_trans ~ Object_contrast + Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## enter_model2: Latency_to_enter ~ Object_contrast * Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## enter_model: Latency_to_enter ~ Object_contrast * Context_contrast + Trial + (1 | NestID) + (-1 + group_dummy | GroupID) + (-1 + ind_dummy + group_dummy | Bird_ID)
##                     npar    AIC    BIC   logLik deviance  Chisq Df Pr(>Chisq)
## enter_model3           8  959.8  994.0  -471.91    943.8                     
## enter_model4_boxcox    8 -127.5  -93.2    71.73   -143.5 1087.3  0           
## enter_model2           9 5148.8 5187.3 -2565.41   5130.8    0.0  1          1
## enter_model           11 5152.8 5199.9 -2565.41   5130.8    0.0  2          1

2) Latency to Eat Model

A similar model is built for Latency_to_Eat, again incorporating interaction terms and random effects:

eat_model <- lmer(log(Latency_to_Eat) ~ Object_contrast * Context_contrast + Trial + 
                    (1 | NestID) + 
                   (- 1 + group_dummy | GroupID) + 
                   (- 1 + ind_dummy + group_dummy | Bird_ID),  
                 data = data)

## boundary (singular) fit: see help('isSingular')

summary(eat_model)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log(Latency_to_Eat) ~ Object_contrast * Context_contrast + Trial +  
##     (1 | NestID) + (-1 + group_dummy | GroupID) + (-1 + ind_dummy +  
##     group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 1636.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1780 -0.5149 -0.1108  0.1927  4.6862 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.78398  0.8854       
##           group_dummy 0.08989  0.2998   1.00
##  NestID   (Intercept) 0.00000  0.0000       
##  GroupID  group_dummy 0.00000  0.0000       
##  Residual             1.00669  1.0033       
## Number of obs: 536, groups:  Bird_ID, 67; NestID, 43; GroupID, 15
## 
## Fixed effects:
##                                   Estimate Std. Error        df t value
## (Intercept)                        1.89202    0.10740 165.73052  17.616
## Object_contrast                    0.74392    0.08668 465.00491   8.583
## Context_contrast                  -1.00808    0.11239  90.13817  -8.969
## Trial                             -0.04274    0.01899 466.49134  -2.251
## Object_contrast:Context_contrast  -0.85108    0.17337 465.00516  -4.909
##                                  Pr(>|t|)    
## (Intercept)                       < 2e-16 ***
## Object_contrast                   < 2e-16 ***
## Context_contrast                 3.94e-14 ***
## Trial                              0.0248 *  
## Object_contrast:Context_contrast 1.27e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.004                     
## Cntxt_cntrs -0.434  0.000              
## Trial       -0.619 -0.007  0.008       
## Objct_cn:C_ -0.008  0.000  0.000  0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

check_model(eat_model)

Similarly, the variance for the (Intercept) under NestID is 0 and the variance for group_dummy under GroupID is 0. Let’s drop those:

eat_model2 <- lmer(log(Latency_to_Eat) ~ Object_contrast * Context_contrast + Trial + 
                   (- 1 + ind_dummy + group_dummy | Bird_ID),  
                 data = data)

## boundary (singular) fit: see help('isSingular')

summary(eat_model2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: log(Latency_to_Eat) ~ Object_contrast * Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 1636.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.1779 -0.5149 -0.1108  0.1927  4.6862 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.78392  0.8854       
##           group_dummy 0.08988  0.2998   1.00
##  Residual             1.00669  1.0033       
## Number of obs: 536, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                   Estimate Std. Error        df t value
## (Intercept)                        1.89202    0.10740 165.74889  17.616
## Object_contrast                    0.74392    0.08668 465.00248   8.583
## Context_contrast                  -1.00808    0.11239  90.14508  -8.969
## Trial                             -0.04274    0.01899 466.48897  -2.251
## Object_contrast:Context_contrast  -0.85108    0.17337 465.00273  -4.909
##                                  Pr(>|t|)    
## (Intercept)                       < 2e-16 ***
## Object_contrast                   < 2e-16 ***
## Context_contrast                 3.94e-14 ***
## Trial                              0.0248 *  
## Object_contrast:Context_contrast 1.27e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.004                     
## Cntxt_cntrs -0.434  0.000              
## Trial       -0.619 -0.007  0.008       
## Objct_cn:C_ -0.008  0.000  0.000  0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

check_model(eat_model2)

There are still some issues with the normality. Let’s remove non participating birds, and try the same boxcox tranformation:

data_eat <- data %>% filter(Latency_to_Eat != 600)

boxcox_transform <- boxcox(lm(Latency_to_Eat ~ Object_contrast * Context_contrast + Trial, data = data))

best_lambda <- boxcox_transform$x[which.max(boxcox_transform$y)]

data_eat$Latency_to_eat_trans <- (data_eat$Latency_to_Eat^best_lambda - 1) / best_lambda



enter_model4_boxcox <- lmer(Latency_to_eat_trans ~ Object_contrast * 
                              Context_contrast + Trial + 
                            (-1 + ind_dummy + group_dummy | Bird_ID), 
                            data = data_eat)
summary(enter_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_eat_trans ~ Object_contrast * Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data_eat
## 
## REML criterion at convergence: -772
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3298 -0.6270 -0.0665  0.5674  3.4392 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.007875 0.08874      
##           group_dummy 0.005565 0.07460  0.92
##  Residual             0.009093 0.09536      
## Number of obs: 506, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                    Estimate Std. Error         df t value
## (Intercept)                        0.782688   0.012637 123.643952  61.936
## Object_contrast                    0.058827   0.008573 375.871518   6.862
## Context_contrast                  -0.153939   0.009588  63.404669 -16.056
## Trial                              0.001207   0.001879 399.950402   0.642
## Object_contrast:Context_contrast  -0.013930   0.017115 377.642252  -0.814
##                                  Pr(>|t|)    
## (Intercept)                       < 2e-16 ***
## Object_contrast                  2.81e-11 ***
## Context_contrast                  < 2e-16 ***
## Trial                               0.521    
## Object_contrast:Context_contrast    0.416    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.042                     
## Cntxt_cntrs -0.186 -0.050              
## Trial       -0.534 -0.039  0.042       
## Objct_cn:C_ -0.041 -0.067  0.056  0.041

check_model(enter_model4_boxcox)

# now without interaction as it's non-sign:
eat_model4_boxcox <- lmer(Latency_to_eat_trans ~ Object_contrast +
                              Context_contrast + Trial + 
                            (-1 + ind_dummy + group_dummy | Bird_ID), 
                            data = data_eat)
summary(eat_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_eat_trans ~ Object_contrast + Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data_eat
## 
## REML criterion at convergence: -777.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3645 -0.6266 -0.0550  0.5560  3.4109 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.007853 0.08862      
##           group_dummy 0.005569 0.07463  0.92
##  Residual             0.009088 0.09533      
## Number of obs: 506, groups:  Bird_ID, 67
## 
## Fixed effects:
##                    Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)        0.782267   0.012621 123.342323  61.981  < 2e-16 ***
## Object_contrast    0.058358   0.008551 376.056191   6.825 3.54e-11 ***
## Context_contrast  -0.153497   0.009564  63.210493 -16.049  < 2e-16 ***
## Trial              0.001270   0.001877 401.021902   0.677    0.499    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_
## Objct_cntrs  0.040              
## Cntxt_cntrs -0.182 -0.047       
## Trial       -0.533 -0.036  0.040

check_model(eat_model4_boxcox)

boxcox model seems to fit data best

eat_model <- lmer(Latency_to_Eat ~ Object_contrast * Context_contrast + Trial + 
                (1 | NestID) + 
                (-1 + group_dummy | GroupID) + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data_eat)

## boundary (singular) fit: see help('isSingular')

eat_model2 <- lmer(Latency_to_Eat ~ Object_contrast * Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data_eat)

## boundary (singular) fit: see help('isSingular')

eat_model3 <- lmer(log(Latency_to_Eat) ~ Object_contrast + Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data_eat)

## boundary (singular) fit: see help('isSingular')

eat_model4_boxcox <- lmer(Latency_to_eat_trans ~ Object_contrast +
                              Context_contrast + Trial + 
                            (-1 + ind_dummy + group_dummy | Bird_ID), 
                            data = data_eat)


anova(eat_model, eat_model2, eat_model3, eat_model4_boxcox)

## refitting model(s) with ML (instead of REML)

## Data: data_eat
## Models:
## eat_model3: log(Latency_to_Eat) ~ Object_contrast + Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## eat_model4_boxcox: Latency_to_eat_trans ~ Object_contrast + Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## eat_model2: Latency_to_Eat ~ Object_contrast * Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## eat_model: Latency_to_Eat ~ Object_contrast * Context_contrast + Trial + (1 | NestID) + (-1 + group_dummy | GroupID) + (-1 + ind_dummy + group_dummy | Bird_ID)
##                   npar    AIC    BIC   logLik deviance  Chisq Df Pr(>Chisq)
## eat_model3           8 1024.9 1058.7  -504.45   1008.9                     
## eat_model4_boxcox    8 -794.8 -761.0   405.39   -810.8 1819.7  0           
## eat_model2           9 5070.9 5108.9 -2526.44   5052.9    0.0  1          1
## eat_model           11 5074.9 5121.4 -2526.44   5052.9    0.0  2          1

3) Time spent in the ZOI

The full model as described in the RR, includes Object_contrast, Context_contrast, and Trial, and a complex random effect structure:

zoi_model <- lmer(Zoi_duration ~ Object_contrast * Context_contrast + Trial + 
                (1 | NestID) + 
                (-1 + group_dummy | GroupID) + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data)

summary(zoi_model)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Zoi_duration ~ Object_contrast * Context_contrast + Trial + (1 |  
##     NestID) + (-1 + group_dummy | GroupID) + (-1 + ind_dummy +  
##     group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 6621.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9343 -0.5729 -0.2174  0.2772  3.5911 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy    5689     75.43       
##           group_dummy  1638     40.47   0.81
##  NestID   (Intercept)   868     29.46       
##  GroupID  group_dummy  1495     38.66       
##  Residual             11668    108.02       
## Number of obs: 536, groups:  Bird_ID, 67; NestID, 43; GroupID, 15
## 
## Fixed effects:
##                                  Estimate Std. Error      df t value Pr(>|t|)
## (Intercept)                       113.131     12.909  89.748   8.764 1.09e-13
## Object_contrast                     3.697      9.332 399.031   0.396    0.692
## Context_contrast                   17.667     14.913  20.537   1.185    0.250
## Trial                               4.116      2.066 412.595   1.992    0.047
## Object_contrast:Context_contrast  106.889     18.664 399.033   5.727 2.01e-08
##                                     
## (Intercept)                      ***
## Object_contrast                     
## Context_contrast                    
## Trial                            *  
## Object_contrast:Context_contrast ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.004                     
## Cntxt_cntrs  0.099  0.000              
## Trial       -0.559 -0.007  0.007       
## Objct_cn:C_ -0.007  0.000  0.000  0.013

check_model(zoi_model)

Here the full model seems to fit, lets try with a simpeler ranef structure though:

zoi_model2 <- lmer(Zoi_duration ~ Object_contrast * Context_contrast + Trial + 
                (-1 +  ind_dummy + group_dummy | Bird_ID), 
              data = data)

summary(zoi_model2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Zoi_duration ~ Object_contrast * Context_contrast + Trial + (-1 +  
##     ind_dummy + group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 6627.5
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.9439 -0.5685 -0.2133  0.2593  3.6214 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy    6452     80.33       
##           group_dummy  4106     64.08   0.70
##  Residual             11668    108.02       
## Number of obs: 536, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                  Estimate Std. Error      df t value Pr(>|t|)
## (Intercept)                       114.606     11.820 157.702   9.696  < 2e-16
## Object_contrast                     3.704      9.332 399.009   0.397   0.6916
## Context_contrast                   18.181     11.711  65.977   1.553   0.1253
## Trial                               3.884      2.054 422.685   1.891   0.0593
## Object_contrast:Context_contrast  106.861     18.664 399.012   5.725 2.03e-08
##                                     
## (Intercept)                      ***
## Object_contrast                     
## Context_contrast                    
## Trial                            .  
## Object_contrast:Context_contrast ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.004                     
## Cntxt_cntrs -0.131  0.000              
## Trial       -0.608 -0.007  0.008       
## Objct_cn:C_ -0.008  0.000  0.000  0.013

check_model(zoi_model2)

There are still issues with the data distribution, let’s boxcox_transform:

boxcox_transform <- boxcox(lm(Zoi_duration+ 0.01 ~ Object_contrast * Context_contrast + Trial, data = data))

best_lambda <- boxcox_transform$x[which.max(boxcox_transform$y)]

data$Latency_to_zoi_trans <- (data$Zoi_duration^best_lambda - 1) / best_lambda

zoi_model4_boxcox <- lmer(Latency_to_zoi_trans ~ Object_contrast * 
                              Context_contrast + Trial + 
                            (-1 + ind_dummy + group_dummy | Bird_ID), 
                            data = data)
summary(zoi_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_zoi_trans ~ Object_contrast * Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 3055.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3475 -0.5434 -0.0239  0.5590  2.5973 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy    7.775   2.788        
##           group_dummy  4.029   2.007    0.66
##  Residual             14.115   3.757        
## Number of obs: 536, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                   Estimate Std. Error        df t value
## (Intercept)                        8.61611    0.40075 166.37905  21.500
## Object_contrast                   -0.71187    0.32457 399.04723  -2.193
## Context_contrast                   1.18531    0.41313  66.00163   2.869
## Trial                              0.22590    0.07144 422.57806   3.162
## Object_contrast:Context_contrast   4.25245    0.64917 399.05046   6.551
##                                  Pr(>|t|)    
## (Intercept)                       < 2e-16 ***
## Object_contrast                   0.02886 *  
## Context_contrast                  0.00552 ** 
## Trial                             0.00168 ** 
## Object_contrast:Context_contrast 1.77e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.004                     
## Cntxt_cntrs -0.174  0.000              
## Trial       -0.624 -0.007  0.008       
## Objct_cn:C_ -0.008  0.000  0.000  0.013

check_model(zoi_model4_boxcox)

Comparing the different models, the boxcox comes out as best:

anova(zoi_model, zoi_model2, zoi_model4_boxcox)

## refitting model(s) with ML (instead of REML)

## Data: data
## Models:
## zoi_model2: Zoi_duration ~ Object_contrast * Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## zoi_model4_boxcox: Latency_to_zoi_trans ~ Object_contrast * Context_contrast + Trial + (-1 + ind_dummy + group_dummy | Bird_ID)
## zoi_model: Zoi_duration ~ Object_contrast * Context_contrast + Trial + (1 | NestID) + (-1 + group_dummy | GroupID) + (-1 + ind_dummy + group_dummy | Bird_ID)
##                   npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)
## zoi_model2           9 6675.8 6714.4 -3328.9   6657.8                     
## zoi_model4_boxcox    9 3070.2 3108.8 -1526.1   3052.2 3605.6  0           
## zoi_model           11 6674.9 6722.0 -3326.4   6652.9    0.0  2          1

So we end up with these models:

# To enter
summary(enter_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_eat_trans ~ Object_contrast * Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data_eat
## 
## REML criterion at convergence: -772
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3298 -0.6270 -0.0665  0.5674  3.4392 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.007875 0.08874      
##           group_dummy 0.005565 0.07460  0.92
##  Residual             0.009093 0.09536      
## Number of obs: 506, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                    Estimate Std. Error         df t value
## (Intercept)                        0.782688   0.012637 123.643952  61.936
## Object_contrast                    0.058827   0.008573 375.871518   6.862
## Context_contrast                  -0.153939   0.009588  63.404669 -16.056
## Trial                              0.001207   0.001879 399.950402   0.642
## Object_contrast:Context_contrast  -0.013930   0.017115 377.642252  -0.814
##                                  Pr(>|t|)    
## (Intercept)                       < 2e-16 ***
## Object_contrast                  2.81e-11 ***
## Context_contrast                  < 2e-16 ***
## Trial                               0.521    
## Object_contrast:Context_contrast    0.416    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.042                     
## Cntxt_cntrs -0.186 -0.050              
## Trial       -0.534 -0.039  0.042       
## Objct_cn:C_ -0.041 -0.067  0.056  0.041

# To eat
summary(eat_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_eat_trans ~ Object_contrast + Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data_eat
## 
## REML criterion at convergence: -777.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.3645 -0.6266 -0.0550  0.5560  3.4109 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy   0.007853 0.08862      
##           group_dummy 0.005569 0.07463  0.92
##  Residual             0.009088 0.09533      
## Number of obs: 506, groups:  Bird_ID, 67
## 
## Fixed effects:
##                    Estimate Std. Error         df t value Pr(>|t|)    
## (Intercept)        0.782267   0.012621 123.342323  61.981  < 2e-16 ***
## Object_contrast    0.058358   0.008551 376.056191   6.825 3.54e-11 ***
## Context_contrast  -0.153497   0.009564  63.210493 -16.049  < 2e-16 ***
## Trial              0.001270   0.001877 401.021902   0.677    0.499    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_
## Objct_cntrs  0.040              
## Cntxt_cntrs -0.182 -0.047       
## Trial       -0.533 -0.036  0.040

# Time near object
summary(zoi_model4_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Latency_to_zoi_trans ~ Object_contrast * Context_contrast + Trial +  
##     (-1 + ind_dummy + group_dummy | Bird_ID)
##    Data: data
## 
## REML criterion at convergence: 3055.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.3475 -0.5434 -0.0239  0.5590  2.5973 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev. Corr
##  Bird_ID  ind_dummy    7.775   2.788        
##           group_dummy  4.029   2.007    0.66
##  Residual             14.115   3.757        
## Number of obs: 536, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                   Estimate Std. Error        df t value
## (Intercept)                        8.61611    0.40075 166.37905  21.500
## Object_contrast                   -0.71187    0.32457 399.04723  -2.193
## Context_contrast                   1.18531    0.41313  66.00163   2.869
## Trial                              0.22590    0.07144 422.57806   3.162
## Object_contrast:Context_contrast   4.25245    0.64917 399.05046   6.551
##                                  Pr(>|t|)    
## (Intercept)                       < 2e-16 ***
## Object_contrast                   0.02886 *  
## Context_contrast                  0.00552 ** 
## Trial                             0.00168 ** 
## Object_contrast:Context_contrast 1.77e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) Objct_ Cntxt_ Trial 
## Objct_cntrs  0.004                     
## Cntxt_cntrs -0.174  0.000              
## Trial       -0.624 -0.007  0.008       
## Objct_cn:C_ -0.008  0.000  0.000  0.013

So for entering:

Fixed Effects:

Object_contrast: Birds took longer to enter when the object was novel. Context_contrast:Birds were quicker to enter when they were in a group compared to when they were alone.

Random Effects:

Variance: The variance is slightly higher for individual trials, suggesting that there is more variability in how long birds take to enter when they are alone. However the variance is only slightly higher.

So for eating:

Fixed Effects:

Object_contrast: Birds take longer to start eating when the object is novel. Context_contrast: Birds are quicker to eat when they are in a group compared to when they are alone.

Random Effects:

Variance: Similar to the latency to enter, there is slightly more variability in the latency to eat during individual trials, indicating that birds’ responses to novelty are more variable when they are alone.

So for ZOI:

Fixed Effects:

Object_contrast: Birds spend less time near novel objects-. Context_contrast: Birds spend more time near objects when they are in a group compared to when they are alone. Trial: Time near objects increases over time. Interaction between Object_contrast and Context_contrast: Suggests that the effect of object novelty on the time spent near the object depends on whether the birds are alone or in a group. In a group, birds may be more willing to spend time near a novel object, while alone, they might avoid it more quickly.

Random Effects:

Variance: The variance is much higher for individual trials, indicating substantial variability in how long individual birds spend near novel objects when they are alone. Potentially reflects differences in individual boldness or fearfulness in the absence of a group.

Additional Analysis

Now fit a multivariate model:

# make data long:
data_long <- data %>%
  pivot_longer(
    cols = c(Latency_to_enter, Latency_to_Eat),
    names_to = "Behaviour_Type",
    values_to = "Latency"
  )
data_long <- data_long %>%
  mutate(
    eat_vs_leave_contrast = case_when(
      Behaviour_Type == "Latency_to_enter" ~ -0.5,
      Behaviour_Type == "Latency_to_Eat" ~ 0.5
    )
  )

# fir full model
latency_model <- lmer(Latency ~ eat_vs_leave_contrast * Object_contrast * Context_contrast + Trial + 
                    (1 | NestID) +
                    (- 1 + group_dummy | GroupID) + 
                    (- 1 + ind_dummy + group_dummy + eat_vs_leave_contrast | Bird_ID), 
                  data = data_long)

## boundary (singular) fit: see help('isSingular')

summary(latency_model)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## Latency ~ eat_vs_leave_contrast * Object_contrast * Context_contrast +  
##     Trial + (1 | NestID) + (-1 + group_dummy | GroupID) + (-1 +  
##     ind_dummy + group_dummy + eat_vs_leave_contrast | Bird_ID)
##    Data: data_long
## 
## REML criterion at convergence: 12715.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0084 -0.2771 -0.0237  0.1790  5.9411 
## 
## Random effects:
##  Groups   Name                  Variance Std.Dev. Corr     
##  Bird_ID  ind_dummy             3278.75  57.260            
##           group_dummy             39.57   6.291   1.00     
##           eat_vs_leave_contrast 1696.89  41.193   1.00 1.00
##  NestID   (Intercept)              0.00   0.000            
##  GroupID  group_dummy              0.00   0.000            
##  Residual                       7916.63  88.975            
## Number of obs: 1072, groups:  Bird_ID, 67; NestID, 43; GroupID, 15
## 
## Fixed effects:
##                                                        Estimate Std. Error
## (Intercept)                                              41.934      6.317
## eat_vs_leave_contrast                                    34.077      7.407
## Object_contrast                                          33.890      5.435
## Context_contrast                                        -37.586      8.265
## Trial                                                    -4.719      1.193
## eat_vs_leave_contrast:Object_contrast                    57.438     10.870
## eat_vs_leave_contrast:Context_contrast                  -50.880     10.870
## Object_contrast:Context_contrast                        -52.068     10.871
## eat_vs_leave_contrast:Object_contrast:Context_contrast  -84.097     21.740
##                                                              df t value
## (Intercept)                                             212.489   6.639
## eat_vs_leave_contrast                                    85.385   4.600
## Object_contrast                                         997.003   6.235
## Context_contrast                                         76.834  -4.547
## Trial                                                  1000.145  -3.954
## eat_vs_leave_contrast:Object_contrast                   997.003   5.284
## eat_vs_leave_contrast:Context_contrast                  997.003  -4.681
## Object_contrast:Context_contrast                        997.004  -4.790
## eat_vs_leave_contrast:Object_contrast:Context_contrast  997.003  -3.868
##                                                        Pr(>|t|)    
## (Intercept)                                            2.60e-10 ***
## eat_vs_leave_contrast                                  1.45e-05 ***
## Object_contrast                                        6.65e-10 ***
## Context_contrast                                       1.99e-05 ***
## Trial                                                  8.22e-05 ***
## eat_vs_leave_contrast:Object_contrast                  1.55e-07 ***
## eat_vs_leave_contrast:Context_contrast                 3.25e-06 ***
## Object_contrast:Context_contrast                       1.92e-06 ***
## eat_vs_leave_contrast:Object_contrast:Context_contrast 0.000117 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) et_v__ Objct_ Cntxt_ Trial  et___:O_ e___:C Ob_:C_
## et_vs_lv_cn  0.418                                                   
## Objct_cntrs  0.004  0.000                                            
## Cntxt_cntrs -0.467 -0.512  0.000                                     
## Trial       -0.661  0.000 -0.007  0.006                              
## et_vs_l_:O_  0.000  0.000  0.000  0.000  0.000                       
## et_vs_l_:C_  0.000  0.000  0.000  0.000  0.000  0.000                
## Objct_cn:C_ -0.009  0.000  0.000  0.000  0.013  0.000    0.000       
## et___:O_:C_  0.000  0.000  0.000  0.000  0.000  0.000    0.000  0.000
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

Same as before, reduce the model:

latency_model2 <- lmer(Latency ~ eat_vs_leave_contrast * Object_contrast * Context_contrast + Trial + 
                    (- 1 + ind_dummy + group_dummy + eat_vs_leave_contrast | Bird_ID), 
                  data = data_long)

## boundary (singular) fit: see help('isSingular')

summary(latency_model2)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## Latency ~ eat_vs_leave_contrast * Object_contrast * Context_contrast +  
##     Trial + (-1 + ind_dummy + group_dummy + eat_vs_leave_contrast |  
##     Bird_ID)
##    Data: data_long
## 
## REML criterion at convergence: 12715.7
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0084 -0.2771 -0.0237  0.1790  5.9411 
## 
## Random effects:
##  Groups   Name                  Variance Std.Dev. Corr     
##  Bird_ID  ind_dummy             3278.78  57.26             
##           group_dummy             39.57   6.29    1.00     
##           eat_vs_leave_contrast 1696.95  41.19    1.00 1.00
##  Residual                       7916.62  88.98             
## Number of obs: 1072, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                                        Estimate Std. Error
## (Intercept)                                              41.934      6.317
## eat_vs_leave_contrast                                    34.077      7.407
## Object_contrast                                          33.890      5.435
## Context_contrast                                        -37.586      8.265
## Trial                                                    -4.719      1.193
## eat_vs_leave_contrast:Object_contrast                    57.438     10.870
## eat_vs_leave_contrast:Context_contrast                  -50.880     10.870
## Object_contrast:Context_contrast                        -52.068     10.871
## eat_vs_leave_contrast:Object_contrast:Context_contrast  -84.097     21.740
##                                                              df t value
## (Intercept)                                             212.491   6.639
## eat_vs_leave_contrast                                    85.383   4.600
## Object_contrast                                         997.004   6.235
## Context_contrast                                         76.832  -4.547
## Trial                                                  1000.145  -3.954
## eat_vs_leave_contrast:Object_contrast                   997.004   5.284
## eat_vs_leave_contrast:Context_contrast                  997.004  -4.681
## Object_contrast:Context_contrast                        997.005  -4.790
## eat_vs_leave_contrast:Object_contrast:Context_contrast  997.004  -3.868
##                                                        Pr(>|t|)    
## (Intercept)                                            2.60e-10 ***
## eat_vs_leave_contrast                                  1.45e-05 ***
## Object_contrast                                        6.65e-10 ***
## Context_contrast                                       1.99e-05 ***
## Trial                                                  8.22e-05 ***
## eat_vs_leave_contrast:Object_contrast                  1.55e-07 ***
## eat_vs_leave_contrast:Context_contrast                 3.25e-06 ***
## Object_contrast:Context_contrast                       1.92e-06 ***
## eat_vs_leave_contrast:Object_contrast:Context_contrast 0.000117 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) et_v__ Objct_ Cntxt_ Trial  et___:O_ e___:C Ob_:C_
## et_vs_lv_cn  0.418                                                   
## Objct_cntrs  0.004  0.000                                            
## Cntxt_cntrs -0.467 -0.512  0.000                                     
## Trial       -0.661  0.000 -0.007  0.006                              
## et_vs_l_:O_  0.000  0.000  0.000  0.000  0.000                       
## et_vs_l_:C_  0.000  0.000  0.000  0.000  0.000  0.000                
## Objct_cn:C_ -0.009  0.000  0.000  0.000  0.013  0.000    0.000       
## et___:O_:C_  0.000  0.000  0.000  0.000  0.000  0.000    0.000  0.000
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

check_model(latency_model2)

Same as before, remove birds that dont enter/eat and boxcox transfrom the data:

data_long_f <- data_long %>% filter(Latency != 600)

boxcox_transform <- boxcox(lm(Latency ~ eat_vs_leave_contrast * Object_contrast * Context_contrast + Trial, data = data_long_f))

best_lambda <- boxcox_transform$x[which.max(boxcox_transform$y)]

data_long_f$Latency_trans <- (data_long_f$Latency^best_lambda - 1) / best_lambda



latency_model3_boxcox <- lmer(Latency_trans ~ eat_vs_leave_contrast * Object_contrast * Context_contrast + Trial + 
                    (- 1 + ind_dummy + group_dummy + eat_vs_leave_contrast | Bird_ID), 
                  data = data_long_f)

summary(latency_model3_boxcox)

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: 
## Latency_trans ~ eat_vs_leave_contrast * Object_contrast * Context_contrast +  
##     Trial + (-1 + ind_dummy + group_dummy + eat_vs_leave_contrast |  
##     Bird_ID)
##    Data: data_long_f
## 
## REML criterion at convergence: -179.8
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.8988 -0.5899 -0.0666  0.4974  3.2599 
## 
## Random effects:
##  Groups   Name                  Variance Std.Dev. Corr       
##  Bird_ID  ind_dummy             0.019321 0.1390              
##           group_dummy           0.005461 0.0739    0.88      
##           eat_vs_leave_contrast 0.011983 0.1095   -0.39 -0.23
##  Residual                       0.039731 0.1993              
## Number of obs: 1039, groups:  Bird_ID, 67
## 
## Fixed effects:
##                                                          Estimate Std. Error
## (Intercept)                                              0.823874   0.017113
## eat_vs_leave_contrast                                    0.353888   0.018258
## Object_contrast                                          0.052793   0.012429
## Context_contrast                                        -0.124633   0.015965
## Trial                                                   -0.030132   0.002731
## eat_vs_leave_contrast:Object_contrast                    0.081287   0.024852
## eat_vs_leave_contrast:Context_contrast                  -0.180206   0.024845
## Object_contrast:Context_contrast                        -0.044359   0.024846
## eat_vs_leave_contrast:Object_contrast:Context_contrast  -0.005870   0.049674
##                                                                df t value
## (Intercept)                                            138.721227  48.143
## eat_vs_leave_contrast                                   64.130732  19.383
## Object_contrast                                        836.101510   4.248
## Context_contrast                                        62.145993  -7.806
## Trial                                                  883.284572 -11.033
## eat_vs_leave_contrast:Object_contrast                  836.166180   3.271
## eat_vs_leave_contrast:Context_contrast                 837.250419  -7.253
## Object_contrast:Context_contrast                       835.307989  -1.785
## eat_vs_leave_contrast:Object_contrast:Context_contrast 835.383555  -0.118
##                                                        Pr(>|t|)    
## (Intercept)                                             < 2e-16 ***
## eat_vs_leave_contrast                                   < 2e-16 ***
## Object_contrast                                        2.40e-05 ***
## Context_contrast                                       8.45e-11 ***
## Trial                                                   < 2e-16 ***
## eat_vs_leave_contrast:Object_contrast                   0.00112 ** 
## eat_vs_leave_contrast:Context_contrast                 9.27e-13 ***
## Object_contrast:Context_contrast                        0.07456 .  
## eat_vs_leave_contrast:Object_contrast:Context_contrast  0.90596    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) et_v__ Objct_ Cntxt_ Trial  et___:O_ e___:C Ob_:C_
## et_vs_lv_cn -0.170                                                   
## Objct_cntrs  0.025  0.020                                            
## Cntxt_cntrs -0.403  0.189 -0.022                                     
## Trial       -0.567 -0.010 -0.023  0.025                              
## et_vs_l_:O_  0.019  0.022  0.034 -0.020 -0.014                       
## et_vs_l_:C_ -0.019 -0.024 -0.025  0.026  0.013 -0.028                
## Objct_cn:C_ -0.026 -0.017 -0.036  0.025  0.028 -0.029    0.029       
## et___:O_:C_ -0.016 -0.019 -0.029  0.023  0.012 -0.035    0.031  0.033

check_model(latency_model3_boxcox)

I would say the multivariate model supports what the we found earlier. Only difference is the significance of trial.